Question

Starting at its rightmost position, it takes 2 seconds for the pendulum of a grandfather clock to swing a horizontal distance of 18 inches from right to left and 2 seconds for the pendulum to swing back from left to right. Which of the following equations models d, the horizontal distance in inches of the pendulum from the center as a function of time, t, in seconds? Assume that right of center is a positive distance and left of center is a negative distance.

Please ignore the check mark!!

Answer 1

the answer is in the picture below :)

Answer 2

Option B is the correct option.

Explanation:

In any cosine function given in the form of y = a cos (bx+c) + d

a = amplitude

b = 2π/period

c = horizontal shift

d = vertical shift

for the case of simple pendulum horizontal and vertical shift will be zero.

So the equation will be in the form of y = a cos (bx)

Here y = d

a = amplitude = 18/2 = 9 (displacement from the center to extreme)

b = 2π/period = 2π/4 = π/2 (period = 4 seconds starting from left-right-left)

Therefore the equation will be d = 9 cos (πt/2)

Option B is the answer.